By 12.45 p.m. (1045 GMT), results reported on the government's VoteInfo App showed 66.94% against the proposal, voted on under the Swiss system of direct democracy, to make protecting the dignity of farm animals such as cattle, chickens and pigs a constitutional requirement.
VoteInfo takes rolling voting results data collated by the Federal Statistics Office and updates constantly from midday.
In a second referendum, the Swiss were narrowly on track to vote in favour of a planned reform of old-age insurance, which among other things would raise the retirement age for women to 65 from 64.
The farming proposal would require the government to set stricter rules for caring for animals, including giving them access to the outdoors, and for slaughtering them. The requirements would also cover imported animals and animal products.
The government recommended against the proposal, saying such changes would breach trade accords, increase investment and operating costs, and boost food prices.
(Writing by Paul Carrel; editing by David Evans)